/**
 * Copyright (c) Facebook, Inc. and its affiliates.
 *
 * This source code is licensed under the MIT license found in the
 * LICENSE file in the root directory of this source tree.
 *
 * BezierEasing - use bezier curve for transition easing function
 * https://github.com/gre/bezier-easing
 *
 * @flow strict
 * @format
 * @copyright 2014-2015 Gaëtan Renaudeau. MIT License.
 */

'use strict';

// These values are established by empiricism with tests (tradeoff: performance VS precision)
const NEWTON_ITERATIONS = 4;
const NEWTON_MIN_SLOPE = 0.001;
const SUBDIVISION_PRECISION = 0.0000001;
const SUBDIVISION_MAX_ITERATIONS = 10;

const kSplineTableSize = 11;
const kSampleStepSize = 1.0 / (kSplineTableSize - 1.0);

const float32ArraySupported = typeof Float32Array === 'function';

function A(aA1, aA2) {
    return 1.0 - 3.0 * aA2 + 3.0 * aA1;
}
function B(aA1, aA2) {
    return 3.0 * aA2 - 6.0 * aA1;
}
function C(aA1) {
    return 3.0 * aA1;
}

// Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
function calcBezier(aT, aA1, aA2) {
    return ((A(aA1, aA2) * aT + B(aA1, aA2)) * aT + C(aA1)) * aT;
}

// Returns dx/dt given t, x1, and x2, or dy/dt given t, y1, and y2.
function getSlope(aT, aA1, aA2) {
    return 3.0 * A(aA1, aA2) * aT * aT + 2.0 * B(aA1, aA2) * aT + C(aA1);
}

function binarySubdivide(aX, _aA, _aB, mX1, mX2) {
    let currentX,
        currentT,
        i = 0,
        aA = _aA,
        aB = _aB;
    do {
        currentT = aA + (aB - aA) / 2.0;
        currentX = calcBezier(currentT, mX1, mX2) - aX;
        if (currentX > 0.0) {
            aB = currentT;
        } else {
            aA = currentT;
        }
    } while (Math.abs(currentX) > SUBDIVISION_PRECISION && ++i < SUBDIVISION_MAX_ITERATIONS);
    return currentT;
}

function newtonRaphsonIterate(aX, _aGuessT, mX1, mX2) {
    let aGuessT = _aGuessT;
    for (let i = 0; i < NEWTON_ITERATIONS; ++i) {
        const currentSlope = getSlope(aGuessT, mX1, mX2);
        if (currentSlope === 0.0) {
            return aGuessT;
        }
        const currentX = calcBezier(aGuessT, mX1, mX2) - aX;
        aGuessT -= currentX / currentSlope;
    }
    return aGuessT;
}

export default function bezier(mX1: number, mY1: number, mX2: number, mY2: number) {
    if (!(mX1 >= 0 && mX1 <= 1 && mX2 >= 0 && mX2 <= 1)) {
        throw new Error('bezier x values must be in [0, 1] range');
    }

    // Precompute samples table
    const sampleValues = float32ArraySupported ? new Float32Array(kSplineTableSize) : new Array(kSplineTableSize);
    if (mX1 !== mY1 || mX2 !== mY2) {
        for (let i = 0; i < kSplineTableSize; ++i) {
            sampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2);
        }
    }

    function getTForX(aX) {
        let intervalStart = 0.0;
        let currentSample = 1;
        const lastSample = kSplineTableSize - 1;

        for (; currentSample !== lastSample && sampleValues[currentSample] <= aX; ++currentSample) {
            intervalStart += kSampleStepSize;
        }
        --currentSample;

        // Interpolate to provide an initial guess for t
        const dist =
            (aX - sampleValues[currentSample]) / (sampleValues[currentSample + 1] - sampleValues[currentSample]);
        const guessForT = intervalStart + dist * kSampleStepSize;

        const initialSlope = getSlope(guessForT, mX1, mX2);
        if (initialSlope >= NEWTON_MIN_SLOPE) {
            return newtonRaphsonIterate(aX, guessForT, mX1, mX2);
        } else if (initialSlope === 0.0) {
            return guessForT;
        } else {
            return binarySubdivide(aX, intervalStart, intervalStart + kSampleStepSize, mX1, mX2);
        }
    }

    return function BezierEasing(x: number): number {
        if (mX1 === mY1 && mX2 === mY2) {
            return x; // linear
        }
        // Because JavaScript number are imprecise, we should guarantee the extremes are right.
        if (x === 0) {
            return 0;
        }
        if (x === 1) {
            return 1;
        }
        return calcBezier(getTForX(x), mY1, mY2);
    };
}
